http://gphjournal.org/index.php/m/issue/feed GPH - International Journal of Mathematics 2021-02-22T11:36:56+00:00 MOHD MUSTAQUE(FranK) editor@gphjournal.org Open Journal Systems <p style="font-family: Helvetica;">The GPH Journal of&nbsp; Mathematics&nbsp;is a an open access journal which publishes research articles, reviews, case studies, guest edited thematic issues and short communications/letters in all areas of mathematics, applied mathematics, applied commutative algebra and algebraic geometry, mathematical biology, physics and engineering, theoretical bioinformatics, experimental mathematics etc.</p> http://gphjournal.org/index.php/m/article/view/371 Our Interesting Journey with The Fascinating Mathematics of the Closed-form Formula of Riemann zeta and eta functions 2021-02-22T11:36:55+00:00 Mulatu Lemma lemmam@savannahstate.edu Agegnehu Atenaand Tilahun Muche noreplygphjournal@gmail.com Wondimu Tekalign noreplygphjournal@gmail.com <p>An explicit identity of sums of powers of complex functions presented via this a closed-form formula of Riemann zeta function produced at any given non-zero complex numbers. The closed-form formula showed us Riemann zeta function has no unique solution for any given non-zero complex numbers which means Riemann zeta function is entirely divergent. Infinitely many zeros of Riemann zeta function produced unfortunately those zeros also gives us non-zero values of Riemann zeta function. Among those zeros, some of them are zeros of Riemann hypothesis. The present paper also discussed on eta function(alternating Riemann zeta function) with exactly the same behavior as Riemann zeta function.</p> 2021-02-22T11:20:13+00:00 ##submission.copyrightStatement## http://gphjournal.org/index.php/m/article/view/377 The Mulatu Numbers in Actions 2021-02-22T11:36:55+00:00 Mulatu Lemma lemmam@savannahstate.edu Latrice Tanksley noreplygphjournal@gmail.com Keisha Brown noreplygphjournal@gmail.com <p>The Mulatu numbers were introduced in [1]. The numbers are sequences of numbers of the form: <strong>4</strong>,<strong>1, 5,6,11,17,28,45</strong><strong>... </strong>&nbsp;The numbers have wonderful and amazing properties and patterns.</p> <p>In mathematical terms, the sequence of the Mulatu numbers is defined by the following <a href="http://en.wikipedia.org/wiki/Recurrence_relation">recurrence relation</a>:</p> <p><img src="/public/site/images/mlemma/recurrence_relation.PNG"></p> <p>The double Angel Formulas for Fibonacci and Lucas numbers are given by the following formulas respectively<strong>.</strong></p> <p><strong><img src="/public/site/images/mlemma/formulas.PNG"></strong></p> <p>Since both the Fibonacci and Lucas numbers have double angle Formulas, It is natural to ask if such formula exists for Mulatu Numbers. The answer is affirmative and produces the following paper.</p> <p><em>2000 Mathematical Subject Classification:&nbsp; 11</em></p> 2021-02-22T11:35:29+00:00 ##submission.copyrightStatement##